Try this:
DSolve[2x[t] t(1+t) x'[t]==1+x[t]^2,x[t],t]
DSolve[x'[t] == (t/x[t])e^(-x[t]/t) + x[t]/t, x[t], t]
DSolve[x'[t] == (t - 4)e^4t + t x[t], x[t], t]
I got outputs from Mathematica in all cases so I think you are in luck.
There are other ways to enter diff equatons into mathematica if the
first method does not work, just like when you solve them by hand often
you have to use a trick or maybe two tricks. (but most often diff eq's
are totally insolvable)
Regards
Peter W
David wrote:
> Is there a method where you can get Mathematica to find general
> solutions for differential equations? For example:
>
> [2xt(1 + t)]dx/dt = 1 + x^2
>
> dx/dt = (t/x)e^(-x/t) + x/t
>
> and
>
> dx/dt = (t - 4)e^4t + tx
>
> I have access to version 4.0
>
> Cheers,
>
> David